Wow, 22 pages of discussion on countersteering!!??
I have been teaching the MSF courses for over 20 years, and to a point I don't try to explain how countersteering works, because a large percentage of people including riders of many years either have no real idea, or cannot grasp the concept, or some claim its a bunch of BS (which it is NOT), or are so LOCKED in their brains to only think go left-STEER left, or right, that they have no chance to ever understand it.
I can explain it, how it works, why it works. But it is far easier to coach people on how to do it and let them feel it for themselves. Once the "feel" of countersteering is developed, all the discussion and theoretical dicsussion is irrelevant for most riders.
Years ago my orthopedic surgeon was a student in my MSF BRC, along with this son and daughter. Now, the man is a doctor, obviously intelligent, but yet he would NOT allow his brain to consider accepting push left-go left/push right-go right when it came to applying countersteering for lean initiation and motorcycle control. He couldn't do it even after I told him not to think about it, just do it and feel/learn the response of the bike. He failed the swerve portion of the training and evaluation and I failed him in the class. I later worked with him one to one and finally got him to feel and accept it did work. His son and daughter easily grasped the concept and passed the class easily. He later did get his license and has been riding for over eight years now.
So, less theory, less discussion. Just DO it and learn from it. It works whenever you need to initiate a lean or change a lean angle (like mid-turn). I have found it still works for dirt riding, and even applies for ice racing.
When life throws you a curve,.....lean into it!